Models and Control of Collective Spatio-Temporal Phenomena in Power Grids

We are asking modern power grids to serve under conditions it was not originally designed for. We also expect the grids to be smart, in how they function, how they withstand contingencies, respond to fluctuations in generation and load, and how the grids are controlled. To meet these ever increasing expectations requires extending power grid models beyond the scope of traditional power engineering.

In this talk aimed at applied mathematicians and physicists I first review basics of power flows, and then outline a number of new problems in modeling, optimization and control theory for smart grids. In particular, I describe new approaches to control of voltage and reactive flow in distribution networks, algorithms to study distance to failure, and statistical analysis of cascading blackouts in transmission networks.